Past events

MSc Hoa Ngo (Aalto U)First passage percolation on mixed sparse random graphs with two types of nodesMonday 20 May 2019, 15:15, M3 (M234)A mixed graph is a graph consisting of both undirected edges and directed edges. This talk discusses first passage percolation on a connected mixed random graph with a given degree sequence, where an undirected edge is formed between type-1 nodes and a directed edge between type-1 and type-2 nodes. Weights on edges are assumed to be independent and exponentially distributed. We analyze a flooding time, which is the minimum time that a uniformly chosen node reaches all other nodes. We derive an asymptotic formula for the flooding time as the number of nodes tend to infinity. As an application, we discuss continuous time information spreading on a random regular graph, where we also take into account the impact of passive nodes. Type-1 nodes can be interpreted as active message spreaders and type-2 nodes can be interpreted as passive receivers which may only receive the message. In this setting we derive an asymptotic formula for the flooding time which is also called the broadcast time in the literature.Aalto Stochastics & Statistics Seminar

Prof. Joerg Kliewer (New Jersey Institute of Technology)Private and Distributed Function ComputationThursday 16 May 2019, 15:15, M3 (M234)We consider the problem of private computation in a distributed storage system. In private computation, a user wishes to compute a function of f messages stored in noncolluding databases while revealing no information about the computation result to the databases. We first employ computation of a linear function of the messages, where linear codes are used to encode the information on the databases. We show that this private linear computation capacity, which is the ratio of the desired linear function size and the total amount of downloaded information, matches the maximum distance separable (MDS) coded capacity of private information retrieval for a large class of linear codes that includes MDS codes. Our converse result is valid for any number of messages and linear combinations, and the capacity expression depends on the rank of the coefficient matrix obtained from all linear combinations. We also present how our linear computation approach can be extended to computing arbitrary multivariate polynomials of the messages. Here, the presented schemes yield improved rates compared to the best known schemes from the literature for a small number of messages, while in the asymptotic case the rates match. ANTA Seminar

Professor Aldo Conca (University of Genova, Italy)Introduction to GrÃ¶bner basesWednesday 15 May 2019, 15:15, M1 (M232)GrÃ¶bner bases and related algorithms can be seen as generalizations of Gaussian elimination for linear systems and Euclid's algorithm for computing polynomial greatest common divisors of univariate polynomials. They can be used to solve algorithmically questions related to polynomials as, for example, the following:
1) deciding whether a system of polynomial equations has solutions,
2) deciding whether a polynomial can be written as linear combinations with polynomials coefficients of given polynomials,
3) deciding whether a polynomial can be written as polynomial function of given polynomials,
4) find the implicit equations of a locus given by a polynomial parametrization.
Questions of this type and their variations have several applications in mathematics, science and engineering.
The goal of the talk is to present a gentle introduction to GrÃ¶bner bases and related algorithms and their use to answer the questions above. Department Colloquium

Giovanni Comi (UHH UniversitÃ¤t Hamburg)A distributional approach to fractional Sobolev spaces and fractional variationWednesday 15 May 2019, 12:15, M3 (M234)Unlike their integer versions, the fractional Sobolev spaces $W^{\alpha, p}(\mathbb{R}^{n})$ do not seem to have a clear distributional nature. By exploiting suitable notions of fractional gradient and fractional divergence already existing in the literature, we introduce the new space $BV^{\alpha}(\mathbb{R}^{n})$ of functions with bounded fractional variation in $\mathbb{R}^n$ of order $\alpha \in (0, 1)$ via a new distributional approach. Thanks to the continuous inclusion $W^{\alpha, 1}(\mathbb{R}^{n}) \subset BV^{\alpha}(\mathbb{R}^{n})$, our theory provides a natural extension of the known fractional framework. In analogy with the classical $BV$ theory, we define sets with (locally) finite fractional Caccioppoli $\alpha$-perimeter and we partially extend De Giorgi's Blow-up Theorem to such sets, proving existence of blow-ups on points of the naturally defined fractional reduced boundary. In addition, we investigate the asymptotic behaviour of these fractional differential operators and we prove that the fractional $\alpha$-variation weakly and Gamma-converges as $\alpha \to 1^{-}$ to the standard De Giorgi's variation.Seminar on analysis and geometry

Dr. Michał Lasoń (Jagiellonian University)On some structures on matroids and related algebraic problemsTuesday 14 May 2019, 15:15, M3 (M234)When an ideal is defined only by combinatorial means, one expects to have a combinatorial description of its algebraic invariants. An attempt to achieve this description often leads to surprisingly deep combinatorial questions. White's conjecture is an example. It asserts that the toric ideal associated to a matroid is generated by quadratic binomials. Another example is a question of Herzog and Hibi about existence of a quadratic Gröbner basis of the toric ideal of a matroid. Both problems reduce to questions about arrangements of bases in a matroid. We will review recent progress and state some intriguing open problems.ANTA Seminar

Prof. Mateusz Michałek (Aalto/Max Planck)From topology to algebraic geometry and back againWednesday 08 May 2019, 15:15, M2 (M233) I will present applications of secant varieties in topology through k-regular embeddings. An embedding of a variety in an affine space is called k-regular if any k points are mapped to linearly independent points. Numeric conditions for the existence of such maps are an object of intensive studies of algebraic topologists dating back to the problem posed by Borsuk in the fifties. Current world record results were obtained by Pavle Blagojevic, Wolfgang Lueck and Guenter Ziegler. Our results relate k-regular maps to punctual versions of secant varieties. This allows us to prove existence of such maps in special cases. The main new ingredient is providing relations to the geometry of the punctual Hilbert scheme and its Gorenstein locus. The talk is based on two joint works: with Jarosław Buczynski, Tadeusz Januszkiewicz and Joachim Jelisiejew and with Christopher Miller: arXiv:1511.05707 and arXiv:1512.00609. ANTA Seminar

Prof Thomas Banchoff (Brown University)Meeting Salvador Dali in the Fourth DimensionThursday 02 May 2019, 15:15, Aalto hallAbstract: How did Salvador Dali choose an unfolded four-dimensional
cross as the central figure in one of his most famous religious
paintings? This talk will describe a ten-year series of meetings with
the artist starting in 1975 and a survey of forty years of
developments in computer graphics approaches to phenomena in four and
higher dimensions.Mathematics and Arts Colloquium

Vesa KaarniojaHigher order QMC rules for uncertainty quantification using periodic random variablesFriday 26 April 2019, 13:00, M3 (M234)A popular model for the parametrization of random fields in
uncertainty quantification is given by the so-called affine model,
where the input random field is assumed to depend on uniformly
distributed random variables in a linear manner. In this talk, we
consider a different -- yet equally valid -- model for the input
random field, where the random variables enter the input field as
periodic functions instead. The field can be constructed to have the
same mean and covariance function as the affine random field. This
setting allows us to construct simple lattice QMC rules that obtain
higher order convergence rates, which we apply to elliptic PDEs
equipped with random coefficients.
This is a joint work with Frances Kuo and Ian Sloan.

Professor Ago-Erik Riet (University of Tartu)Permutation CodesThursday 25 April 2019, 11:15, M140 (Majakka)Codes over permutations can potentially be applied for error correction in flash memories. Information in a flash memory is stored as electric charge in memory cells. Permutation codes are useful to combat errors of charge leakage over time and overshoot while writing. In this approach, within a block of numbered cells all charges are assumed to be different and their relative ranking defines a permutation.
Various distance metrics can be defined in the symmetric group of all permutations over the set $\{1,2,\ldots,n\}$, used to define codes, with varying degrees of usefulness to flash memories.
In this talk I review some of my work with coauthors on permutation codes for error correction. I also review a potential source coding into permutations framework proposed by us. I also introduce multipermutation codes which is a possible relaxation of permutation codes to the case when some charges within the block can be equal. I briefly discuss the difficulties of encoding information into and decoding from permutations.ANTA Seminar

Professor Vitaly Skachek (University of Tartu)Constructing Asynchronous Batch Codes using HypergraphsTuesday 23 April 2019, 15:15, M1 (M232)Batch codes were first proposed by Ishai et al. as a means for balancing load in distributed storage systems. They are also of potential use in private information retrieval. In this talk, we present a new variant of batch codes termed "asynchronous batch codes", which are designed for parallel recovery of information symbols from the coded database, where different requests take different service time (i.e. the requests are served in an asynchronous manner).
It turns out that the graph-based batch codes studied by Rawat et al. are asynchronous. By building on the ideas therein, we show that hypergraphs of Berge girth at least 4 yield graph-based asynchronous batch codes. We prove the hypergraph-theoretic proposition that the maximum number of hyperedges in a hypergraph of a fixed Berge girth equals the quantity in a certain generalization of the hypergraph-theoretic (6,3)-problem. We then apply the constructions and bounds by Erdos, Frankl and Rodl to obtain batch code constructions and bounds on the optimal redundancy of the graph-based asynchronous batch codes.
We show that the optimal redundancy $\rho(k)$ of graph-based asynchronous batch codes of dimension $k$ with the query size $t=3$ is $2\sqrt{k}$. Moreover, for a general fixed value of $t \ge 4$, $\rho(k) = O\left({k}^{1/(2-\epsilon)}\right)$ for any small $\epsilon > 0$. For a general value of $t \ge 4$, $\lim_{k \rightarrow \infty} \rho(k)/\sqrt{k} = \infty$.
(Joint work with Ago-Erik Riet and Eldho K. Thomas) Department Colloquium

Karl Brustad (NTNU, Trondheim)Segre's Theorem. An analytic proof of a result in differential geometry.Wednesday 10 April 2019, 12:15, M3 (M234)Seminar on analysis and geometry

Dr. Jie LiHigh-Rate MDS Code Constructions for Distributed Storage SystemsTuesday 02 April 2019, 15:15, M3 (M234)NOTE: TUESDAY!
Distributed storage systems with high reliability have wide applications in large data centers, peer-to-peer storage systems, and storage in wireless networks. To ensure reliability, the redundancy is crucial for these systems. A popular option to introduce redundancy is to employ erasure codes such as MDS (Maximum Distance Separable) codes, which can efficiently store data and protect against node failures. In this talk, we will introduce several novel high-rate MDS code constructions which have optimal repair bandwidth and some other key properties. In addition, two generic transformations for MDS codes will also be given, one is to enable optimal repair in MDS code and the other is to reduce the sub-packetization level of existing MDS codes, which address two major concerns in high-rate MDS codes for DSSs.ANTA seminar

Professor Paavo Pylkkänen (University of Helsinki)Explaining consciousness in terms of informationTuesday 26 March 2019, 16:15, M1 (M232)Conscious experience has become the focus of intensive interdisciplinary study over the past few decades. By now there are a number of candidate theories of consciousness, many of which make use of notions of information in their attempted explanations of consciousness. This talk provides first a brief overview of consciousness studies and then considers how consciousness can be understood in the light of two approaches that make an appeal to information: David Bohms active information approach, and Giulio Tononis mathematical integrated information theory of consciousness.Department Colloquium

Dr Elena Magnanini (U Modena)On the scaled cumulant generating function of the triangle observable in the dense Erdӧs-Rényi modelThursday 21 March 2019, 10:15, M3 (M234)Further informationThe computation of the probability of rare events is the main purpose of large deviations theory. For instance, in a simple case, one can consider the rare event in which a sum of i.i.d. Bernoulli variables attains a value which is larger than its average. A completely different and much more difficult problem, is the computation of large deviations probability of nonlinear functionals of the Bernoulli variables, e.g. cubic polynomials. A case in which such nonlinear problems arise is, for instance, the study of complex networks. In this talk I will present the behavior of the so-called scaled cumulant generating function of the number of triangles of an Erdӧs-Rényi random graph (dense case). The scaled cumulant generating function is strictly connected with the theory of large deviations since, when it is possible to apply the Gärtner-Ellis theorem, it turns out to be the Legendre transform of the rate function. More precisely, the aim of this talk is twofold. On one hand, to describe a modified version of a known Monte Carlo method, called Cloning algorithm, tailored for approximating the scaled cumulant generating function of an additive observable in the framework of random graphs. One the other hand, keeping the focus on the triangle observable, to present the numerical investigation performed in the region where the analytical expression of such function is not known (replica breaking regime).

Prof. Christine Kelley (University of Nebraska-Lincoln)Communicating over channels with partial erasuresWednesday 13 March 2019, 15:15, M3 (M234)Channels with partial erasures were recently introduced to characterize erasure events in applications where some partial information about an erased symbol or packet is known. After some background on partial erasure channels, we will introduce a multilevel coding scheme for designing codes over these channels. We also characterize cases of channel parameters when capacity can be achieved using such a scheme. Time permitting, we will look at fountain codes over partial erasure channels as well as simple relay channels where at least one link is a partial erasure channel.
ANTA seminar

Prof. Simon Blackburn (Royal Holloway)The Walnut Digital Signature AlgorithmThursday 07 March 2019, 10:15, M3 (M234)NOTE different day and time!
Walnut is a digital signature algorithm that was first proposed in 2017 by Anshel, Atkins, Goldfeld and Gunnells. The algorithm is based on techniques from braid group theory, and is one of the submissions for the high-profile NIST Post Quantum Cryptography standardisation process. The talk will describe Walnut, and some of the attacks that have been mounted on it. No knowledge of cryptography or the braid group will be assumed. Based on joint work with Ward Beullens (KU Leuven).ANTA seminar

Marcus GreferathSpectral Methods for Coding Theory in a non-commutative SetupTuesday 26 February 2019, 15:15, M1 (M232)In many areas of Electrical Engineering, Computer Science, and Applicable mathematics, and particularly in Algebraic Coding Theory, there are impressive examples, showing how a discrete Fourier calculus can be used in order to construct codes of prescribed minimum distance. Here, this spectral technique is basically restricted to cyclic codes over finite fields so far, however there are no strict reasons to keep it restrained to this case. This talk is particularly interested in the scenario, where a non-commutative finite group acts on the co-ordinate domain, while the alphabet of the desired code may be a finite ring. We will sketch the successful development of a Fourier Calculus for this setting and observe a few remarkable facts. This is work in progress! world.Department Colloquium

Dr. Tefjol Pllaha (ELEC)Equivalence of Quantum Stabilizer CodesWednesday 20 February 2019, 15:15, M2 (M233)In the first part of the talk we will describe basic notions in quantum computation with a view toward error-correction. We will describe in detail Shor's 9 qubit code, and then motivate an algebraic approach to the stabilizer formalism. In the second part of the talk we will define stabilizer codes over Frobenius rings and point out why MacWilliams Extension Theorem fails in this case. The latter motivates the study of isometry groups, for which we show how to construct stabilizer codes with predetermined isometry groups. If time permits, we will end with some remarks on the LU-LC conjecture.ANTA seminar

Prof. Colin Boyd (Norwegian University of Science and Technology)Bitcoin, Blockchains and Smart Contracts: Understanding the Crypto in CryptocurrenciesWednesday 06 February 2019, 17:30, Lumituuli Auditorium, Dipoli, Otakaari 24, 02150 EspooCryptocurrencies and blockchains are the most widely publicized applications of cryptography today. Using the example of Bitcoin, we will aim to understand the cryptographic building blocks of cryptocurrencies and how they fit together to enable a distributed payment system. We will then explore why newer cryptocurrencies built on Bitcoin employ more advanced cryptography. In particular we will examine the contentious issue of anonymous payments. Finally we will discuss the concept of smart contracts, how they can be achieved using blockchains, and what kinds of applications they may be useful for.HAIC Talks

Jaakko LehtinenSimulation + machine learning = interpretable, less data hungry AI?Tuesday 29 January 2019, 15:00, A2How do we make computers perceive the everyday world and deeply understand it just by looking at it? How do we build virtual agents and real robots that build on this perception and are able to move and interact with the world, including us humans, in a natural manner? In this talk, Ill talk about the currently accelerating congruence of physically-based simulation and machine learning in solving very hard problems in artificial intelligence. Ill argue that the classic approach of merely learning from human-labeled examples is doomed  there is simply no way for us to cover all the variability in the real world with annotated examples  and that making use of interpretable models (simulators!) in the learning process is the way forward. Ill give examples of my own work, as well as that of my close colleagues and collaborators, and other highlights from around the world.
Department Colloquium

Dr. Justyna SzpondFermat-type configurations in projective spacesWednesday 23 January 2019, 15:00, M2 (M233)A Fermat arrangement of lines in the complex projective plane is given by linear
factors of the polynomial $(x^n-y^n)(y^n-z^n)(z^n-x^n)$ for some $n\geq 3$.
Singular points of these arrangements have appeared recently in commutative algebra, more precisely in the containment problem between symbolic and ordinary powers of homogeneous polynomials and in algebraic geometry in the theory of linear systems and unexpected hypersurfaces. I will explain these two appearances and present considerable generalizations which led to substantial, new results in both fields.

Dr. Tomasz SzembergLinear systems with assigned base lociWednesday 23 January 2019, 14:00, M2 (M233)I will report on special linear systems on complex projective spaces. Even though
the topic is classical and studied for more than 100 years, many important questions are not answered in a satisfactory way.Algebra Seminar

Istvan PrauseArctic curves beyond the arctic circleMonday 17 December 2018, 15:00, M3 (M234)The dimer model studies random configurations of perfect matchings (dimer covers) of bipartite planar graphs. Through an associated height function such a configuration is encoded in a random surface. These random surfaces (with a fixed boundary) exhibit limit shape formation: a deterministic limit surface emerges in the macroscopic limit. The imposed boundary condition can have dramatic effect: in certain regions the dimers line up in an ordered fashion (form a frozen facet) and do not look random at all. A prime example of this phenomenon is the arctic circle of domino tilings of the Aztec diamond from 1995.
We now have, mostly due to Kenyon et al., a general theory which describes these phenomena in unprecedented detail. The limit shape is described by a convex but singular and degenerate variational problem with a gradient constraint. These features are responsible for facet formation and the appearance of arctic curves. In the talk, I will use the lozenge tiling model (dimer model on the hexagonal lattice) to showcase these issues and address how one can analyse the variational problem.Aalto Stochastics and Statistics seminar / Ilmonen, Kytölä, Leskelä

Michele Miranda (University of Ferrara)Properties of convex sets in Wiener spacesWednesday 05 December 2018, 12:00, M3 (M234)We show some recent results on convex sets in Wiener spaces. We characterize the essential and reduced bound- ary of open convex sets and investigate integration by parts formulae. Of particular interest is the investigation of trace theorems for functions of bounded variation on boundaries of subsets in Wiener spaces.
Seminar on analysis and geometry

Eveliina Peltola (University of Geneva)Crossing Probabilities of Multiple Ising InterfacesMonday 03 December 2018, 15:15, M3 (M234)Crossing Probabilities of Multiple Ising Interfaces
The planar Ising model is one of the most studied lattice models in statistical physics. Exhibiting a continuous phase transition, it enjoys conformal invariance in the scaling limit, as has been verified recently in celebrated works initiated by S. Smirnov. In this talk, I discuss crossing probabilities of multiple interfaces in the critical Ising model with alternating boundary conditions. In the scaling limit, they are conformally invariant expressions given by so-called pure partition functions of multiple SLE(kappa) with kappa=3.
I also describe analogous results for critical percolation and the Gaussian free field.
Joint work with Hao Wu (Yau Mathematical Sciences Center, Tsinghua University)Aalto stochastics and statistics seminar / Ilmonen, Kytölä, Leskelä

Prof Tuomo Kuusi (University of Helsinki)Quantitative Stochastic Homogenization and Large-Scale RegularityTuesday 27 November 2018, 15:15, EOne of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonlocal functions of the former. In our recent book, jointly with S. Armstrong and J.-C. Mourrat, we have addressed this problem from a new perspective. Essentially, we use recently developed regularity theory for stochastic homogenization to accelerate the weak convergence of the energy density, flux and gradient of the solutions as we pass to larger and larger length scales, until it saturates at the CLT scaling. I will discuss our approach and give, at the same time, an informal introduction to our book.Department Colloquium

Negin KarimiGeneralized regenerating codes and security of distributed storage systemWednesday 21 November 2018, 15:15, M3 (M234)Traditional regenerating codes are efficient tools to optimize both storage and repair bandwidth in storing data across a distributed storage system, particularly in comparison to erasure codes and data replication. In traditional regenerating codes, the collection of any k nodes can reconstruct the information file and is called the reconstruction set, N_R. Also, a failed node can be regenerated from any d surviving nodes. These collections of d nodes are called the regeneration sets, N_H. The number of reconstruction sets and the number of regeneration sets satisfies N_R= C_n^k and N _H=C_{n-1}^d, where C_n^k denotes "n choose k". In generalized regenerating codes, we will have, 1 \le N_R \le C^k_n and 1 \le N_H \le C_{n-1}^d. In this talk, I address the problem of secure generalized regenerating codes and present a coding scheme by focusing on the features of the generalized regenerating codes that protect data in the distributed storage system in presence of an active omniscient adversary.ANTA seminar

Aleksis Koski (University of Jyväskylä)Sobolev homeomorphic extensionsWednesday 21 November 2018, 12:15, M3 (M234)In the mathematical theory of nonlinear elasticity one typically represents elastic bodies as domains in Euclidean space, and the main object of study are deformations (mappings) between two such bodies. The class of acceptable deformations one considers usually consists of Sobolev homeomorphisms between the respective domains, for example, with some given boundary values. It is hence a fundamental question in this theory to ask whether a given boundary map admits a homeomorphic extension in the Sobolev class or not. We share some recent developments on this subject, including sharp existence results and counterexamples.Seminar on Analysis and Geometry

Olga KuznetsovaMSc thesis presentation: Private information retrieval with arbitrary collusion patternsWednesday 07 November 2018, 15:15, M3 (M234)In coded Private Information Retrieval (PIR), a user wants to download a file from a coded database without revealing the identity of the file. We consider the setting where certain subsets of servers collude to deduce the requested file. These subsets form an abstract simplicial complex called the collusion pattern. In this talk we will discuss the combinatorics of the general star product scheme for PIR under the assumption that the database is encoded using a repetition code.
Advisor Ragnar Freij-Hollanti, supervisor Camilla Hollanti. ANTA Seminar

Vito Buffa (University of Ferrara)New insights into BV Functions and Integration by Parts Formulæ in Metric Measure SpacesWednesday 07 November 2018, 12:15, M3 (M234)The starting point of our discussion is a notion of BV functions tailored for RCD(K,\infty) metric measure spaces, which makes use of suitable vector fields.
This definition motivates both the study of integration by parts formulæ in terms of essentially bounded divergence-measure vector fields in diverse metric settings, and an investigation of the issue of traces of BV functions
in the context of a doubling metric measure space supporting a Poincaré inequality.
Based on joint works with G. E. Comi (Scuola Normale Superiore, Pisa) and M. Miranda Jr (University of Ferrara).Seminar on analysis and geometry

Vitaly Skachek (University of Tartu)[NOTE the unusual time and place!] Batch and PIR Codes and Their Connections to Locally Repairable CodesMonday 05 November 2018, 14:15, M205In this survey talk, we discuss two related families of codes: batch codes and codes for private information retrieval. These two families can be viewed as natural generalizations of locally repairable codes, which were extensively studied in the context of coding for fault tolerance in distributed data storage systems. Bounds on the parameters of the codes, as well as basic constructions, are presented. Connections between different code families are discussed.ANTA Seminar

Prof Chris Brzuska (Aalto University)Proof Theory for CryptographyTuesday 30 October 2018, 15:15, EMost of our cryptography is not perfectly unbreakable. Given enough time, one could, theoretically, perform an exhaustive search over the key space and e.g., decrypt messages intended for another receiver. Modern cryptography, thus, relies on computationally hard problems that (are conjectured to) require an exorbitant amount of computation to solve. Complex systems such as TLS, the backbone of secure communication on the internet, rely on quite a number of such hard problems, and the protocol itself has a specification of over 100 pages. The relation between the protocol security (in a model) and the underlying assumptions needs to be established via a rigorous reduction proof. Due to the complexity of the protocols, the reduction proofs for modern protocols escape what a human can grasp. Therefore, in recent years, the proofs have been partially delegated to computers which, to be fair, also struggle with the tremendous complexity. We propose a new level of abstraction that allows to recover human understanding of security reductions for complex protocols and show how to apply it to the new TLS 1.3 standard (ongoing work).
Joint work with Ben Dowling, Antoine Délignat-Lavaud, Cédric Fournet, Konrad Kohbrok & Markulf Kohlweiss Department Colloquium

Prof. Luka Grubisic, University of ZagrebAnalysis of an eigenvalue problem on a metric graphFriday 26 October 2018, 14:15, M2 (M233)We analyze a second order constrained eigenvalue problem on a metric graph. The underlying vector valued differential operator originates in the vibration analysis in the modelling of endovasular stents. We also study the dynamical problem for such a configuration and show that standard DAE integrators can solve the problem well. This is a joint work with V. Mehrmann and J. Tambaca.

Razane Tajeddine and Lukas HolzbaurOn private keyword and stream searchWednesday 24 October 2018, 15:15, M3 (M234)In the first part of the talk, we discuss private keyword search (PKS). Some work has been done to ensure privacy for the user when searching for keywords from a distributed storage system.
In the second part of the talk, we discuss the concept of private search on streaming data (PSS), and its connection to PIR and PKS on the example of a scheme given by Ostrovsky et al. The problem of private search on streaming data (PSS) has been considered under various cryptographic assumptions, e.g. by means of homomorphic cryptosystems and public-key program obfuscation. ANTA seminar

Hans Tylli (University of Helsinki)Structural rigidity of generalised Volterra operators on Hardy spacesWednesday 24 October 2018, 12:15, M3 (M234) will describe generalised analytic Volterra operators T_g on the Hardy spaces H^p
over the unit disk D for 1 \le p < \infty, where
T_gf(z) = \int_0^z f(w)g'(w) dw,
for z in D and f in H^p. Above the analytic map g from BMOA is the symbol of T_g.
The systematic study of this class of operators was initiated by Aleman, Cima and
Siskakis around 1995. Earlier certain T_g were used by Pommerenke (1977)
and the class contains e.g. a version of the classical Cesaro averaging operator,
which is obtained with g(z) = - \log(1-z).
I will focus attention on recent work on the structural rigidity of the class of
non-compact operators T_g on H^p for p different from 2.
The main result says that if T_g defines an isomorphism from M to T_g(M)
for the infinite-dimensional closed subspace M of H^p,
then M contains a subspace linearly isomorphic to the sequence space \ell^p.
In particular, this implies that the non-compact Volterra operators T_g have a
quite restricted range of linear qualitative behaviour compared to that of
arbitrary bounded operators on H^p (for p different from 2).
This is joint work with Santeri Miihkinen (Åbo), Pekka Nieminen (Turku) and
Eero Saksman (Helsinki).Seminar on Analysis and Geometry

Vasiliki Evdoridou (The Open University, UK)Singularities of inner functions and entire maps of finite orderWednesday 17 October 2018, 12:15, M3 (M234)Let f be a transcendental entire function of finite order and U an unbounded, invariant Fatou component of f. We can associate an inner function, g say, to the restriction of f to U. We will show that for two classes of entire functions whose set of singular values is bounded, the number of singularities of g on the unit circle is at most twice the order of f. This is joint work with N. Fagella, X. Jarque and D. Sixsmith.Seminar on analysis and geometry

Arttu Karppinen (University of Turku)Higher integrability of the gradient of a minimizer with generalized Orlicz growthWednesday 10 October 2018, 12:15, M3 (M234)In this talk we prove global higher integrability of a minimizer of an obstacle problem with generalized Orlicz growth conditions. This recovers the similiar results of the special cases such as polynomial, variable exponent and double phase growth.Seminar on Analysis and Geometry

Christoph Scheven (University of Duisburg-Essen)The obstacle problem for the porous medium equation: Existence and regularity resultsWednesday 26 September 2018, 12:15, M3 (M234)In the talk we will present some results on existence and regularity of solutions to the obstacle problem associated to the porous medium equation. In particular, we will report on recent results concerning the higher integrability of the spatial gradient of solutions.Seminar on analysis and geometry

Prof Matthieu Jonckheere (University of Buenos Aires)Distance learning using Euclidean percolation: Following Fermat's principleTuesday 25 September 2018, 15:15, EIn unsupervised statistical learning tasks such as clustering, recommendation, or dimension reduction, a notion of distance or similarity between points is crucial but usually not directly available as an input. We discuss recent techniques to infer a metric from observed data. Then we propose a new density-based estimator for weighted geodesic distances that takes into account the underlying density of the data, and that is suitable for nonuniform data lying on a manifold of lower dimension than the ambient space. The consistency of the estimator is proven using tools from first passage percolation. After discussing its properties and implementation, we evaluate its performance for clustering tasks. Department Colloquium

Verena Bögelein (University of Salzburg)Higher integrability for doubly nonlinear evolution equationsWednesday 19 September 2018, 12:15, M3 (M234)In this talk we establish the higher integrability of the spatial gradient of weak solutions to doubly nonlinear evolution equations.Seminar on analysis and geometry

Jens Zumbrägel (Universität Passau)Indiscrete Logarithms?Thursday 13 September 2018, 15:15, M2 (M233)The modern public-key cryptography, as originated from the seminal work
by Diffie and Hellman, is since connected with the difficulty of the
discrete logarithm problem. However, for finite fields of small
characteristic, this problem turns out to be not as intractable as
thought for a long time. In fact, some striking observations have
recently led to considerable record computations and severe consequences
for the security of certain cryptosystems. This talk aims to illustrate
the main mathematical ideas behind these rather new developments.ANTA seminar

Prof. Stefano Giani (Durham)High-Order/hp-Adaptive Multilevel Discontinuous Galerkin MethodsTuesday 04 September 2018, 14:00, M2 (M233)After a brief introduction on discontinuous Galerkin (DG) methods I describe the DG composite finite element (DGCFE) method, a DG multilevel method with hp-adaptivity. The main advantage of this multilevel method is that the number of degrees of freedom of the finite element space is independent of the presence of complicated or tiny features in the domain. In other words, even on a very complicated domain, an approximation of the solution can be computed with only a fistful of degrees of freedom. Unlikely other multilevel methods, this method does not perturb the problem, in the sense that the problem solved on the coarse mesh is always a discretization of the DG weak form of the problem, no matter how coarse the mesh is.
The hp-adaptivity algorithm for the DGCFE method is completely automatic and capable of exploiting both local polynomial-degree-variation (p-refinement) and local mesh subdivision (h-refinement), thereby offering greater flexibility and efficiency than numerical techniques which only incorporate h-refinement or p-refinement alone.
Two types of error estimators are used to drive the adaptivity: an explicit one and an implicit one based on a duality argument. In the latter case, the element residuals of the computed numerical solution are multiplied by local weights involving the solution of a certain dual or adjoint problem.
The performance of the hp-refinement algorithm is demonstrated through a series of numerical experiments.
DGCFE can also be used to solve problems on polygonal meshes. This will be shown for elliptic eigenvalue problems.

Marco Fiorucci (Ca' Foscari U, Venice)Graph Summarization Using Regular PartitionsThursday 30 August 2018, 11:15, M3 (M234)The world we live in is becoming more and more interconnected and huge amounts of data are produced and stored every day by different interrelated entities. This high-throughput generation calls for the development of efficient algorithms to understand and process large and noisy network data. To address this challenging task, we develop a principled approach to summarize (compress) large graphs based on regular partitions, the existence of which was first established in a celebrated result proved by Endre Szemerédi in the mid-1970. A regular partition is defined as a partition of the vertex set into a bounded number of random-like bipartite graphs, called regular pairs. In particular, a regular pair is a highly uniform bipartite graph in which the density of any reasonably sized subgraphs is about the same as the overall density of the bipartite graph.
In this talk, I will provide an overview of the regularity lemma and will discuss its potential usefulness in real-world applications.Aalto Stochastics & Statistics Seminar

Sung Chul Park (EPFL)Local correlations in the critical and near-critical planar Ising modelWednesday 15 August 2018, 14:15, M3 (M234)The scaling limit of the 2D critical Ising model is expected to exhibit conformal invariance, which has been proved in the case of spin (Chelkak, Hongler and Izyurov 2015) and energy (local 2-point) correlations (Hongler and Smirnov 2013). We extend these results by giving a conformally covariant description for the local n-point correlations in the scaling limit. Then we will go on to discuss preliminary results and ongoing work in the near-critical (scaling towards criticality) setting and their significance from the viewpoint of Conformal Field Theory. Based on joint work with R. Gheissari (first part) and C. Hongler.Stochastics seminar / Ilmonen, Kytölä, Leskelä

Kalle Kytölä [Math physics afternoon]Probabilistic lattice models and conformal field theoryWednesday 08 August 2018, 16:30, M3 (M234)A major conjecture in two-dimensional statistical mechanics is that scaling limits of lattice models are described by conformally invariant quantum field theories. The main ingredient of conformal field theories is a Virasoro algebra representation on local fields. In two lattice models, the critical Ising model and the discrete Gaussian free field, we find this exact structure even before passing to the scaling limit.
The result is joint work with Clément Hongler (EPFL) and Fredrik Viklund (KTH).Mathematical physics afternoon organized by Karrila & Kytölä

Christian Webb [Math physics afternoon]On the eigenvalues of a random Hermitian matrixWednesday 08 August 2018, 16:00, M3 (M234)I will discuss some recent work concerning rigidity of eigenvalues of a random Hermitian matrix: that is, how much can the eigenvalues of a large random Hermitian matrix fluctuate around certain deterministic quantities.Mathematical physics afternoon organized by Karrila & Kytölä

David Radnell [Math physics afternoon]Moduli spaces in conformal field theoryWednesday 08 August 2018, 15:30, M3 (M234)One of the standard axiomatic approaches to conformal field theory involves infinite-dimensional moduli spaces of Riemann surfaces. The rigorous definition and study of these moduli spaces requires complex analysis and geometry, quasiconformal Teichmueller theory, functional analysis etc. I will outline the connection between these topics and state some recent results.
Mathematical physics afternoon organized by Karrila & Kytölä

Alex Karrila [Math physics afternoon]On the weak convergence of multiple plane curvesWednesday 08 August 2018, 14:30, M3 (M234)In statistical mechanics, one often studies a random model on a fine-mesh lattice approximating a continuum domain. One descriptive feature of such models are interface curves, such as boundaries of magnetization clusters in a ferromagnetism model. Consider a situation where boundary conditions, for instance alternating +/- magnetizations on the boundary of the ferromagnet, force the existence of multiple macroscopic chordal interfaces. We derive criteria, valid for various random models, that guarantee the existence of a weak limit of such chordal interfaces as the lattice mesh turns finer. Mathematical physics afternoon organized by Karrila & Kytölä

Armando Gutierrez [Math physics afternoon]On the metric compactification of Banach spacesWednesday 08 August 2018, 14:00, M3 (M234)I will explain a method that has recently appeared in metric geometry and has shown to be an effective technique to compactify metric spaces. Afterwards, I will present a complete description of the metric compactification of the classical Banach spaces Lp in finite and infinite dimensions.Mathematical physics afternoon organized by Karrila & Kytölä

Osama Abuzaid [Math physics afternoon]Infinite self avoiding half space random walks [MSc talk]Wednesday 08 August 2018, 12:30, M3 (M234)A self avoiding walk (SAW) is an injective walk in a lattice embedded in an Euclidean space. A random SAW of length n is a uniformly distributed random variable on all self avoiding walks of length n starting from origin. In this talk, we are mainly interested in random SAWs in a d-dimensional qubic lattice which are restricted to the upper half plane. These are called self avoiding half space random walks (SAHSW). I will present necessary tools to show the existence of an infinite random SAHSW which is defined as the limit of random SAHSWs of length n, as n tends to infinity.Mathematical physics afternoon organized by Karrila & Kytölä

Pihla Karanko MSc thesis presentation: Protocol verification in Tamarin in an access sharing applicationWednesday 25 July 2018, 15:15, M3 (M234)I study the use of formal methods in protocol verification, in particular Tamarin language. Tamarin (https://tamarin-prover.github.io) is an automated symbolic verification tool for security protocols. It allows you to specify a protocol and its security properties using so called facts, rewrite rules and lemmas. You can then use it to check the validity of the security properties.
In the talk I explain the theory and syntax of Tamarin and show how to use it to specify and validate a part of an access protocol. I work for a company called Bitwards that provides access sharing software for electronic locks and the protocol I am going to present is part of their access sharing system that we want to formally validate.
MSc thesis presentation. Thesis work is carried out at Bitwards. Advisor Chris Brzuska, supervisor Camilla Hollanti.
ANTA seminar